Question

What happens to the resistance of A wire if its length decreases?

Answer 1

When the length of a wire decreases, its resistance also decreases.

Here’s why: Resistance (\(R\)) in a wire depends on the following factors:

1. Length of the wire (\(L\))
   

1. Cross-sectional area of the wire (\(A\))
   

1. Resistivity of the material (\(\rho\))
   

The formula for resistance is:

\[
R = \rho \times \frac{L}{A}
\]

1. \(L\) is the length of the wire.
   

1. \(A\) is the cross-sectional area of the wire.
   

1. \(\rho\) is the resistivity of the material (which is a property of the material itself).
   

So, if the length (\(L\)) of the wire decreases, the resistance decreases as well because resistance is directly proportional to the length. In simpler terms, the shorter the wire, the fewer obstacles there are for the current to pass through, so the current can flow more easily, and resistance is lower.

This is true as long as the material and the cross-sectional area of the wire stay the same.